I wouldn't worry about the floors too much. Definitely didn't think about them when I solved this.
×The key is to let the stalwart get directly next to a mud blob, and then distract the seep he's heading for. He'll then switch targets, rotating his sword and hitting the blob.
However, as the stalwart moves before seep, he'll take one step before he turns, so you need to account for that.
If you've worked all that out already and just can't seem to get further:
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×Perhaps the issue is in which seep get killed first.